Depends on the credit card. That is indeed how some cards work, but there are better deals than that for sure.
My advice to people who are just starting their free travel endeavors via credit cards, is to first figure out where you are most likely to travel (domestically or internationally), then figure out which airline is the easiest for you to use (are you near a hub airport for any airlines?). With that info, you can decide which airline's card you should be applying for.
For example, I used to live in the DC area, so having United miles was great for international travel, because of their hub at Dulles. For domestic travel, Southwest has a hub at BWI. Good deals frequently come up for both of those airlines, so wife and I applied for multiple cards with both airlines. You can usually get 50,000 miles per card, so we would each get both a personal and business credit card. With 2 airlines to do that with, it adds up quickly. Southwest was especially benevolent to us, especially with their companion pass.
Goal is not to simply get points/miles, but rather to find the most efficient way to get a free trip that you want.